The previous section showed that by interpreting the conformal prediction output as the contour function that defines a full consonant plausibility function, a strong validity property can be achieved, one that goes beyond coverage probabilities of prediction regions. This connection between conformal prediction and consonant plausibility functions suggests that insights about conformal prediction can be gained from the perspective of imprecise probabilities—in particular, random sets, possibility measures, etc. In this section, we show that there is an alternative route to “conformal + consonance” as described above, through the IM framework, due to [1]}, [2]}, based on distributions of random sets. This connection to IMs provides a new, imprecise probability-based characterization of conformal prediction.
